Of course. I've also noticed that the installer remains in the background after I click Quit. I'll try to reboot again.
I have two Windows 10s on the first one I had no problem installing Qt 5.6 RC. On the second one (in a different office and different ISP) it won't work.

To me it looks you have already your answer. When it is still working on one computer, but not on another, it has obviously somethig to do with your second computer. Since this is on another ISP, that might be the reason.
To locate the actual reason you may exchange the computers, if possible.

@Zingam
Assuming that you have on both windows 10 machines the same Qt installation, where should be the problem?
One is working the other is not. The only solution I see is a reinstall of Qt on the failing machine.

I have no Qt installation on that Machine and no crapware (only Windows defender). It is quite clean installation - Visual studio 2015, Chrome, Firefox, VLC player and Sony SDKs, Tortoise SVN... I don't remember anything else significant that would change the system. Is there a log or something that I can check what's going on?

Just to make it clear: I am attempting a new clean installation on Windows 10. Windows was installed cleanly a couple of months ago and runs without any issues.